Some Reflections on Analysis of High-Frequency Data

Finance is arguably the most empirically oriented of all the social sciences. This is in part due to the deliberate practical orientation and the ready availability of high-quality financial market data. In recent years, the ever lower costs of data recording and storage have driven the phenomenon to the ultimate limit for some markets: We may have access to time-stamped observations on all quotes and transactions, denoted ultra-high-frequency data by Engle (in press). These data are of direct interest for market microstructure issues dealing with the price discovery process, the market infrastructure, the strategic behavior of market participants, and the modeling of real-time market dynamics. Moreover, the advent of ultra-high-frequency data poses interesting challenges to empirical work, and it has inspired the developments of new econometric and statistical tools dealing with such complications as a random daily number of time series observations with a random time between arrivals. In addition, the discrete price grid can distort inference concerning the asset price dynamics at the highest frequencies. Finally, any price series now has an associated string of natural conditioning variables-for example, volume, news, time of day, time between transactions or quotes, concurrent prices of similar assets, and so forth. Although current work is making strides on all these fronts, how to deal with the majority of these jointly is still an open question. Interesting surveys of the literature were provided by Hasbrouck (1996), Goodhart and O'Hara (1997), and Engle (in press). As such, the ability of high-frequency data to provide information about market microstructure issues is well recognized. Because the other participants in this discussion undoubtedly will discuss these developments, I shall instead concentrate my brief remarks on a different use of highfrequency data that is perhaps, as of yet, less appreciated-namely, the ability of such data to shed new light on issues concerning the distribution of lower-frequency speculative returns.

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